Conventionally, polymers employed in tire components include diene rubbers such as natural rubber (NR), polybutadiene (BR), polyisoprene (IR), and styrene-butadiene copolymer rubber. The traction, tread wear, and rolling resistance of a tire is to some extent dependent upon the dynamic viscoelastic properties of the polymers utilized in making the tire tread. However, optimizing the formulation to improve one of these properties frequently leads to a decline in the other properties. For example, skid resistance and traction characteristics may be improved while sacrificing tread wear or rolling resistance. Thus, a blend of polymers is often employed in order to balance the desired properties of the tire tread.
For example, U.S. Pat. No. 6,437,205 teaches a blend of low molecular weight high-cis polybutadiene and high molecular weight high-cis polybutadiene for use in pneumatic tire treads. The low molecular weight fraction has a number average molecular weight of from about 2 to about 50 kg/mol. The high molecular weight fraction has a number average molecular weight of from about 90 to about 300 kg/mol. The tread exhibits improved fracture properties, snow traction, weight traction, and rolling resistance.
Polymer compositions typically include a plurality of polymer molecules characterized by a variety of sizes or chain lengths. In other words, polymeric compositions typically include a plurality of polymeric molecules that have a variety of molecular weights. The degree of molecular weight differentiation within a polymeric composition can be analyzed and is often referred to as polydispersity. Polydispersity can result from the nature of the catalyst and the polymerization conditions employed in the synthesis of the polymer.
Polymer size or molecular weight is conventionally determined by using Gel Permeation Chromotagraphy with a set of standards, which for example can be supplied by a set of polystyrene standards. This analysis provides a molecular weight distribution that can be represented in the form of a histogram or a continuous curve. In general, the x-axis of the distribution curve may be some direct or indirect measure of the degree of polymerization of the polymer being analyzed, which may be molecular weight, chain length, radius of gyration, intrinsic viscosity or any other property related to molar mass. In general, the y-axis of the distribution curve may be any direct or indirect measure of the amount or concentration of polymer present, which may be the number or weight of polymer molecules, refractive index, turbidity, and the like. The distribution curve may be expressed in many different forms depending upon the functions that are plotted.
It is often useful to characterize a polymer composition using an average size or molecular weight. It is also useful to quantify the distribution around this average value. For example, polymer compositions are often characterized by a weight average molecular weight (Mw) and a number average molecular weight (Mn). The polydispersity may be represented by the Mw/Mn determinations. When a polymer is monodisperse, i.e., where each molecule has the same length or molecular weight, the Mw and Mn are the same, and therefore the Mw/Mn of the polymer is one, and the peak of the curve (Mp) will be same molecular weight as the weight average (Mw) and number average (Mn) molecular weights of the polymer. As those skilled in the art appreciate, monodisperse polymers are generally a theoretical consideration and attempts to make them have thus far required very special circumstances.
Analysis can also be made of the modality of the distribution curve. Monomodal polymers are characterized by one peak in the molecular weight distribution curve. Where the Mw/Mn is greater than one, the peak will typically exist between the weight average (Mw) and number average (Mn) molecular weights of the polymer. It also therefore mathematically follows that the weight average molecular weight (Mw) will be greater than the number average molecular weight (Mn).
Determination of the peak molecular weight (Mp) can be mathematically determined. As is mathematically known, the peak on a curve is where the slope of the curve equals zero; i.e. the location on the curve that has neither a positive or negative slope. In the case of a monomodal distribution, the Mp corresponds to a point on the curve where the slope of the curve changes from positive to negative or vice versa.
In view of this, the first derivative of the molecular weight distribution curve will have a value of zero at the Mp point of the distribution curve. For example, the peak may be defined by the expressiondW/dM=0where W is the weight of a polymer and M is the molecular mass or weight.
Monomodal polymers will have a zero at one point while multi-modal polymers will have two or more points in their distribution where the first derivative is zero. For example, a bimodal polymer can have three points in its distribution where the first derivative is zero, which points correspond to the two Mp peaks and the third corresponding to the valley between the peaks. Or, bimodal polymers that do not include a valley between the Mp peaks (which may occur in the case of a first peak having a shoulder), then the curve will include two points where the first derivative is zero, the first point corresponding to the Mp of the first peak and the second corresponding to the Mp of the shoulder.